This would be somewhat similar to Costco's model, where most (all?) of employee wages come from membership card fees, not product revenue. With this model, you could still let people donate 100% of their funds to the patient if they wanted.
You could even make a slider with an animation that displays the percent which goes to each part of your business - so 10% or 15% of the donation could goto administration.
I love your idea, it's tremendous. Good luck!
This is a great idea. Check the Humble Bundle's (http://www.humblebundle.com/) sliders at the bottom of the page to see how they handle their "Humble Tip", maybe you guys can do something similar.
Maybe make it 'what is the max percent you want to see spent on admin cost'. that way you are allowed to use as much as you'd like to for the patient.
You never know!